Self-tuning or adaptive controllers are known in the control art and have been implemented in many specialized applications. The introduction of microprocessor technology has enabled self-tuning or adaptive process controllers to become a significant commercial reality.
Proper tuning of a controller is not only essential to the correct operation thereof, but also affords a commensurate improvement in product quality, scrap reduction, decreased down-time and economical operation of the process and/or apparatus controlled by the controller. Procedures for tuning conventional Proportional, Integral and Derivitive (hereinafter PID) controllers are well established and relatively simple to perform, but are often time-consuming. The replacement of a controller, or a significant component thereof, as well as a portion of the apparatus being controlled, requires re-tuning of the controller. Such re-tuning often is very difficult and requires considerable knowledge and skill of the process operator. Some controllers have digital settings for the three control parameters, Proportional Band (PB), Integral Time Constant (ITC) and Derivative Time Constant (DTC), which simplifies the reproduction of the correct control parameter settings when a controller is replaced, for example. However, such digital settings are not of any assistance if, for example, a controlled heater element is changed, or the mechanics of the controlled system are appreciably altered. The associated controller in such instances requires re-tuning.
Most conventional temperature controllers, whether analog or microprocessor-based, are three-term, PID controllers. In such PID controllers the control algorithm is based on a proportional gain, an integration action and a derivative action. On more refined and complex controllers, relative cool gain adjustment and a parameter for overshoot inhibition are provided.
As used herein, Gain, or more commonly Proportional Band, PB, simply amplifies the error between a desired setpoint and a measured value to establish a proper power level. The term PB expresses the controller gain as a percent of the span of the controller. For example, a 25% PB equates to a gain of 4; a 10% PB is a gain of 10, etc. Thus a controller with a span of one thousand degrees and a PB of 10% defines a control range of one hundred degrees around setpoint. Also, if the measured value is twenty-five degrees below setpoint, the output level will be twenty-five percent. The PB determines the magnitude of the response to an error. If the PB is too small (high gain) the controlled system could oscillate because it is over-reponsive to the controller. However, a wide PB (low gain) may result in control "wander" due to a lack of responsiveness of the controlled system. The "ideal" control situation is achieved when the PB is as narrow as possible without causing oscillation.
Integral Action, or Automatic Reset, is probably the most important factor governing control at setpoint. The Integral term (I) slowly shifts the output level as a result of an error between setpoint and the measured value. If the measured value is below the setpoint the Integral Action will gradually increase the output power level in an attempt to correct this error. The adjustment of Integral Action is normally in the form of a time constant or the Integral Time Constant, ITC.
The longer the ITC, the more slowly the power level of the controlled heater is shifted. Alternatively, if the Integral term is set to a fast value, the heater power level could be shifted too quickly, thereby inducing oscillation as the controller is attempting to control faster than the load can change. Conversely, an ITC that is too long results in very sluggish control. Lengthening the ITC results in markedly slower response, but the overshoot is substantially eliminated as the control settles to the setpoint.
Derivative Action, or Rate, provides a sudden shift in output power level as a result of a sudden or quick change in the Measured Value, MV. Should the MV drop quickly, the derivative term provides a large change in the output level in an attempt to correct the perturbation before it goes too far. Derivative Action is the most beneficial control action in causing a controlled system to recover from small perturbations.
Derivative Action is usually associated with overshoot inhibition rather than with transient response. In fact, Derivative Action should not be used to curb overshoot on start-up because the steady-state performance of the controller is seriously degraded. A separate parameter such as Approach Control is normally used to prevent overshoot and is independent of the PID tuning values and does not affect their performance. By using such a variable overshoot inhibition parameter, a system can be set up for optimum steady-state response and the overshoot can be eliminated as desired.
Each implementation of a PID algorithm behaves in a slightly different manner because of the subtle variations in the controller's algorithm. For example, some controllers may provide excellent overshoot inhibition as an inherent characteristic, or perhaps superior response to setpoint changes. These are some of the factors that may make one controller more suitable than another for a particular system to be controlled.
The introduction of microprocessors to control technology has greatly increased the flexibility of controllers as is known to the controller art. For example many control parameters, such as for example, overshoot inhibition, might have been built into an anaog type controller in an unalterable way. With the use of a microprocessor such a control parameter is now adjustable.
There are several established and well known techniques for evaluating and determining the control characteristics and parameters of controlled loops and systems and which are adaptable to the design of self-tuning controllers. For example, to name a few, there are the Model Reference Approach, the ON/OFF Control Approach, the Process Reaction Curve Technique, the Ziegler-Nichols Step Response Method, and the Ziegler-Nichols Closed-Loop Cycling Method. Of these classical control theory approaches, the two most common are the Process Reaction Curve Technique (PRCT) and the Closed-Loop Cycling Method (CLCM). While other approaches are known, and could conceivably be adapted to the design of self-tuning controllers, the preferred control technique used in designing and developing the self-tuning controller of this invention is the CLCM for reasons discussed more fully herein. However, it is to be understood that the self-tuning controller of this invention can be adapted to any control theory approach using the techniques disclosed and described herein.
Control techniques other than those specifically enumerated above do exist. For example, modern control theory, with the State-Variable Concept, could be used, but is considered to be too complex for adaptation to the type 810 Microprocessor-Based 3-Term Controller that has been adapted using the self-tuning concepts disclosed and described herein and forming the basic concepts of this invention. Moreover, the State-Variable Concept may not be commercially viable, as the marketplace, at the time of this invention, has accepted the PID approach to controller design. A well-tuned PID controller affords near optimum performance which could not be significantly improved by, for example, the State-Variable approach.
Another control technique is Gain-Scheduling but that technique merely uses parameters, such as Gain or PB, which are adjusted according to prearranged criteria. That does not enable adjustment of the self-tuned controller for unknown loads, for example, and therefore is not a self-tuning algorithm in the context of that disclosed and claimed herein.
Auto-Correlation and Cross-Correlation techniques can also be used to advantage to extract process characteristics blurred by noise, but such correlation techniques are slow to respond since they require many sampling periods to deduce operating parameters for control purposes. However, such techniques could be employed in designing a self-tuning controller in accordance with the concepts and principles of the present invention in those applications where such slow response was acceptable. Such adaptation would require significantly more memory capacity than is available in the 810 type controller described herein and which has been modified to incorporate the self-tuning techniques described and disclose herein.
Other control techniques include those used by 'educated and sophisticated" system operators in which the control loops of a controlled system are tuned manually. Such manual tuning techniques involve observing the response of the system under certain conditions and calculating the control parameters from a set of formulas, which are typically fairly simple. Such manual techniques, which are software-adaptable or implementable, could be termed "automated tuning", wherein the computer or microprocessor automates the operator manipulations. Such methods result in tuning constants that are reasonably optimal in any given situation, but not necessarily perfect, as they are based on certain assumptions and approximations. But they achieve satisfactory pragmatic results.
The PRCT and CLCM control theory design techniques introduced by Ziegler and Nichols in an article entitled "Optimum Settings for Automatic Controllers"; Transactions of A.S.M.E.; November, 1942; pp 759-767, defined "optimal tuning" as being achieved when the controlled system responds to a perturbation with a 4:1 decay ratio. For example, given an initial perturbation of +40.degree., the controller's subsequent response would yield an undershoot of -10.degree., followed by an overshoot of +2.5.degree.. Such a definition of "optimal tuning" may not suit every application and therefore the "tradeoffs" must be understood.
The 4:1 decay ratio criteria of Ziegler-Nichols is adopted herein solely for the purpose of describing the self-tuning principles of the invention. Other criteria are applicable to the self-tuning techniques described herein, and the scope of the invention is not intended to be limited by such criteria.
The principles of PRCT are shown in FIG. 1 and require that the controller is removed from the control loop or system and a step perturbation injected into the loop or system. The perturbation has a level that is convenient and non-damaging to the system, but should be introduced when the system is stable at ambient temperature. The time L is often referred to as the Lag Time and is considered to be the time necessry to overcome the thermal inertia of the load being heated. A straight line drawn tangent to the process reaction curve at the point of inflection has a slope R as shown in FIG. 1. From the slope R and Lag Time L, the PID values may be calculated by the following equation. EQU PB=RL/P.times.100%/(span)
where TI=2 L and TD=0.5 L. It is noted that PB is expressed as percent of instrument span, whereas TI and TD are time constants expresed in minutes. P is the percent power level used as the step input divided by 100 (expressed as a fraction).
G. H. Cohen and G. A. Coon modified the PRCT technigue to yield a more thorough evaluation. Their contributions to such techniques are exemplified in the following publications: (1) "Theoretical Consideration of Retarded Control; Transactions of A.S.M.E.; July 1953; pp 827-833; (2) "How to Find Controller Settings from Process Characteristics"; G. A. Coon; Control Engineering; May 1956; pp 66-76; and (3) "How to Set Three-Term Controllers"; G. A. Coon; Control Engineering; June 1956; pp 71-75.
Exemplary results are illustrated in FIG. 2, where T is the final attained temperature expressed as a percent of span of the controller as a result of the step input P; and P is the step input of power expressed as a percent of maximum allowable power; and K=T/P. The results of the evaluation are shown in FIG. 2 and Table I below.
TABLE I __________________________________________________________________________ INTEGRAL TIME DERIVATIVE CONTROLLER PROPORTIONAL BAND CONSTANT TIME CONSTANT __________________________________________________________________________ Proportional only ##STR1## Proportional plus Integral ##STR2## ##STR3## Proportional plus Derivative ##STR4## ##STR5## Proportional, Integral and Derivative ##STR6## ##STR7## ##STR8## __________________________________________________________________________
It is again noted that the goal in the above Ziegler-Nichols techniques and the Cohen-Coon techniques is to obtain a 4:1 decay ratio, which may not be suitable for all applications. For example, to reduce overshoot and lengthen the settling time, the PB and ITC should be increased.
In the CLCM, a Proportional-Only controller (no Integral or Derivative terms) is placed in oscillation by setting the PB to a very small value such that the control loop will cycle with a characteristic frequency. The characteristic system oscillation frequency is a very accurate representation of the system's responsiveness and therefore can be used to derive the controller time constants as is well known to those skilled in the system control art.
An outline of the procedure for the CLCM follows:
1. Eliminate Integral and Derivative action from the controller. PA1 2. Reduce the PB until the control loop oscillates and measure the period of oscillation, T. PA1 3. Widen PB until the process is just slightly unstable. This value of PB, P, is referred to as the point of "ultimate sensitivity". PA1 4. Table II below provides the values of Pb, TI and TD. PA1 1. Determine optimal values of PB, Integral Time Constant (ITC) and Derivative Time Constant (DTC). PA1 2. Require no operator attention. PA1 3. Attain the required operating tmperatures as quickly as possible without any overshoot. PA1 4. Allow a forced re-tune if required or desired. PA1 5. Retain the tuning parameters in non-volatile memory so that tuning need not be performed after a short duration power failure. PA1 6. Allow manual over-ride of the self-tuning function. PA1 1. The system tunes above ambient within the linear portion of the operating range; and PA1 2. Tuning occurs below setpoint to avoid overshoot.
TABLE II ______________________________________ PRO- INTEGRAL DERIVATIVE PORTIONAL TIME TIME CONTROLLER BAND CONSTANT CONSTANT ______________________________________ Proportional 2P only Proportional 2.2P .8T plus Integral Proportional 1.67p .5T .12T plus Integral and Derivative ______________________________________
The settings in Table II establish control with a 4:1 decay ratio which may provide too much overshoot for some processes or applications. Table III provides guidelines for altering the values in Table II when using Proportional, Integral and Derivative terms.
TABLE III ______________________________________ PRO- INTEGRAL DERIVATIVE CONTROL PORTIONAL TIME TIME ACTION BAND CONSTANT CONSTANT ______________________________________ Underdamped P .5T .125T Critically 1.5P T .167T Damped Overdamped 2P 1.5T .167T ______________________________________
These values have been used in the response curve shown in FIG. 3.
The CLCM, or Ziegler-Nichols Closed-Loop Cycling Method, involves placing the loop or system in oscillation, which could be damaging because of the repeated overshoot and undershoot, which may in some instances be excessive. The Cohen and Coon PRCT evaluates the process near ambient and therefore could provide a misrepresentation of the process response at setpoint. Many processes change their characteristics with the application of heat. For example, in furnace applications there is a shift from convection heating to radiant heating at higher temperatures. Plastics machinery behaves in an entirely different manner when cold than when it is at operating temperature and is full of plasticized material under extreme pressure. For the aforementioned, as well as other, reasons it is at least desirable, if not essential, to tune a control loop when it is at operating temperature.
Perhaps the most commonly used technique for tuning a loop is to manually set parameter values based on operator experience, and then observe the results. While that method may be excellent for "fine-tuning" a controller, it usually requires an extensive amount of experience to be commercially useful.
As has been stated repeatedly above, the Ziegler-Nichols and Cohen-Coon tehniques are based on a 4:1 decay ratio, which is generally considered to be somewhat too oscillatory for the temperature control of plastics machinery. Frequently in plastics machinery applications, the engineer setting up the process determines how the temperature controller should respond to various perturbations. Thus, it is evident that the control algorithm of a self-tuning controller is extremely critical in achieving desirable, much less optimal, control of a process or system.
Another aspect of self-tuned controllers is that the control algorithm is often tailored for a certain industry's application and requirements, and therefore is limited in its range of control applications as it can only optimally control a specific type load. Moreover, since most self-tuned controllers generate a Derivative setting, they cannot be used for tuning transport lags, such as diameter control loops or air flow systems. There is also a limit to the adjustment range of the PID parameters so that the controller may not be applicable to loads which are very fast or have a high gain.
A self-tuning controller affords considerable advantages in the time involved in tuning a particular control loop because it can repeat a tuning procedure reliably when significant process changes are made or the controller is replaced, without requiring the control operator to carefully monitor the performance. That is the primary advantage of self-tuned controller.
Self-tuning control algorithms are programmed into microprocessors which are capable of generating the control signals to follow the algorithm step-by-step, make decisions based on data obtained from peripheral measuring or sensing devices, and to perform calculations required by the self-tuning algorithm. Certain of the control techniques described above utilize step-by-step procedures and require simple measurements and calculations. If the PRCT of Ziegler and Nichols is adapted for the self-tuning procedure, the assumption is made that the Lag Time calculated at ambient temperature relates to the system time constants at operating temperature. The controlled zone or area can be place under ON/OFF control for several periods of oscillation to establish the tuning parameters, providing that the system or process under control can tolerate such oscillations. A self-tuning controller may also attempt to model the load being controlled to determine the control parameters and constants for the tuning procedure. Such self-tuning controllers are apt to be quite expensive because of the memory and storage capacity required for the model program. Additionally, such control systems generally require that the operator respond to a number of questions prior to, or during, tuning.